Subgroups — C₃×#41404 #10660011

Order 768.

2586 conjugacy classes of subgroups.

The subgroup lattice has 1004 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₃×#546	C₂	1	2	yes	maximal, complemented
2	C₃×#2817	C₂	1	1	yes	maximal, characteristic, complemented
3	C₃×#2812	C₂	1	1	yes	maximal, characteristic, complemented
4	C₃×#2717	C₂	1	2	yes	maximal, complemented
5	C₃×#2708	C₂	1	2	yes	maximal, complemented
6	C₃×#2688	C₂	1	2	yes	maximal, complemented
7	C₃×#2686	C₂	1	2	yes	maximal, complemented
8	C₃×#2638	C₂	1	2	yes	maximal, complemented
9	C₃×#2622	C₂	1	2	yes	maximal, complemented
10	C₃×#2617	C₂	1	1	yes	maximal, characteristic, complemented
11	C₃×#2600	C₂	1	1	yes	maximal, characteristic, complemented
12	C₃×#2483	C₂	1	1	yes	maximal, characteristic, complemented
13	C₃×#2444	C₂	1	2	yes	maximal, complemented
14	C₃×#2430	C₂	1	2	yes	maximal, complemented
15	C₃×#2419	C₂	1	2	yes	maximal, complemented
16	C₃×#2412	C₂	1	2	yes	maximal, complemented
17	C₃×#2406	C₂	1	2	yes	maximal, complemented
18	C₂×C₃×#397	C₂	1	1	yes	maximal, characteristic, complemented
19	C₃×#2308	C₂	1	1	yes	maximal, characteristic, complemented
20	#41404	C₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
21	C₂²×C₃×#41	C₂²	1	2	yes	—
22	C₂³×C₃×D₄	C₂²	1	1	yes	characteristic
23	C₃×#546	—	2	16	no	—
24	C₂×C₃×#124	C₂²	1	2	yes	—
25	C₂×C₃×#123	C₂²	1	2	yes	—
26	C₂×C₃×#123	C₂²	1	2	yes	—
27	C₂×C₃×#123	C₂²	1	2	yes	complemented
28	C₂×C₃×C₂²⋊Q₈	C₂²	1	2	yes	—
29	C₂×C₃×#121	C₂²	1	2	yes	—
30	C₂×C₃×#121	C₂²	1	2	yes	—
31	C₂×C₃×#121	C₂²	1	2	yes	—
32	C₂×C₃×#121	C₂²	1	1	yes	characteristic, complemented
33	C₂×C₃×#120	C₂²	1	2	yes	—
34	C₂×C₃×#120	C₂²	1	2	yes	—
35	C₂×C₃×C₄×D₄	C₂²	1	2	yes	—
36	C₂×C₃×C₄×D₄	C₂²	1	2	yes	—
37	C₂²×C₃×C₄⋊C₄	C₂²	1	1	yes	characteristic, complemented
38	C₂²×C₃×C₂²⋊C₄	C₂²	1	2	yes	—
39	C₂²×C₃×C₂²⋊C₄	C₂²	1	2	yes	—
40	C₂²×C₃×C₂²⋊C₄	C₂²	1	1	yes	characteristic
41	C₂²×C₃×C₂²⋊C₄	C₂²	1	1	yes	characteristic
42	C₃×#400	C₂²	1	2	yes	complemented
43	C₃×#400	C₂²	1	2	yes	complemented
44	C₃×#398	C₂²	1	2	yes	complemented
45	C₃×#397	C₂²	1	1	yes	characteristic
46	C₃×#397	C₂²	1	2	yes	—
47	C₃×#397	C₂²	1	2	yes	—
48	C₃×#397	C₂²	1	2	yes	—
49	C₃×#397	C₂²	1	1	yes	characteristic
50	C₃×#397	C₂²	1	1	yes	characteristic
51	C₃×#397	C₂²	1	1	yes	characteristic, complemented
52	C₃×#397	C₂²	1	2	yes	complemented
53	C₃×#397	C₂²	1	2	yes	complemented
54	C₃×#397	C₂²	1	2	yes	complemented
55	C₃×#397	C₂²	1	1	yes	characteristic, complemented
56	C₃×#397	C₂²	1	2	yes	complemented
57	C₃×#397	C₂²	1	1	yes	characteristic, complemented
58	C₃×#397	C₂²	1	2	yes	complemented
59	C₃×#395	C₂²	1	2	yes	complemented
60	C₃×#395	C₂²	1	2	yes	complemented
61	C₃×#395	C₂²	1	2	yes	complemented
62	C₃×#394	C₂²	1	2	yes	—
63	C₃×#394	C₂²	1	2	yes	—
64	C₃×#394	C₂²	1	2	yes	—
65	C₃×#394	C₂²	1	2	yes	complemented
66	C₃×#394	C₂²	1	2	yes	complemented
67	C₃×#394	C₂²	1	2	yes	complemented
68	C₃×#394	C₂²	1	2	yes	complemented
69	C₃×#394	C₂²	1	2	yes	complemented
70	C₃×#393	C₂²	1	2	yes	complemented
71	C₃×#392	C₂²	1	1	yes	characteristic
72	C₃×#392	C₂²	1	1	yes	characteristic, complemented
73	C₃×#392	C₂²	1	2	yes	complemented
74	C₃×#388	C₂²	1	2	yes	complemented
75	C₃×#387	C₂²	1	2	yes	complemented
76	C₃×#387	C₂²	1	2	yes	complemented
77	C₃×#387	C₂²	1	2	yes	complemented
78	C₃×#386	C₂²	1	2	yes	—
79	C₃×#386	C₂²	1	2	yes	—
80	C₃×#386	C₂²	1	2	yes	—
81	C₃×#386	C₂²	1	2	yes	—
82	C₃×#386	C₂²	1	2	yes	complemented
83	C₃×#386	C₂²	1	2	yes	complemented
84	C₃×#386	C₂²	1	2	yes	complemented
85	C₃×#386	C₂²	1	2	yes	complemented
86	C₃×#386	C₂²	1	2	yes	complemented
87	C₃×#386	C₂²	1	2	yes	complemented
88	C₃×#386	C₂²	1	2	yes	complemented
89	C₃×#385	C₂²	1	2	yes	complemented
90	C₃×#385	C₂²	1	2	yes	complemented
91	C₃×#385	C₂²	1	2	yes	complemented
92	C₃×#385	C₂²	1	2	yes	complemented
93	C₃×#385	C₂²	1	2	yes	complemented
94	C₃×#385	C₂²	1	2	yes	complemented
95	C₃×#385	C₂²	1	2	yes	complemented
96	C₃×#385	C₂²	1	2	yes	complemented
97	C₃×#381	C₂²	1	1	yes	characteristic
98	C₃×#381	C₂²	1	1	yes	characteristic
99	C₃×#381	C₂²	1	2	yes	complemented
100	C₃×#381	C₂²	1	2	yes	complemented
101	C₃×#381	C₂²	1	2	yes	complemented
102	C₃×#380	C₂²	1	1	yes	characteristic, complemented
103	C₃×#380	C₂²	1	2	yes	complemented
104	C₃×#380	C₂²	1	2	yes	complemented
105	C₃×#379	C₂²	1	1	yes	characteristic
106	C₃×#379	C₂²	1	1	yes	characteristic
107	C₂×C₃×#95	C₂²	1	2	yes	complemented
108	C₂×C₃×#95	C₂²	1	1	yes	characteristic, complemented
109	C₂×#546	C₂×C₃	1	2	yes	complemented
110	#2817	C₂×C₃	1	1	yes	characteristic, complemented
111	#2812	C₂×C₃	1	1	yes	characteristic, complemented
112	#2717	C₂×C₃	1	2	yes	complemented
113	#2708	C₂×C₃	1	2	yes	complemented
114	#2688	C₂×C₃	1	2	yes	complemented
115	#2686	C₂×C₃	1	2	yes	complemented
116	#2638	C₂×C₃	1	2	yes	complemented
117	#2622	C₂×C₃	1	2	yes	complemented
118	#2617	C₂×C₃	1	1	yes	characteristic, complemented
119	#2600	C₂×C₃	1	1	yes	characteristic, complemented
120	#2483	C₂×C₃	1	1	yes	characteristic, complemented
121	#2444	C₂×C₃	1	2	yes	complemented
122	#2430	C₂×C₃	1	2	yes	complemented
123	#2419	C₂×C₃	1	2	yes	complemented
124	#2412	C₂×C₃	1	2	yes	complemented
125	#2406	C₂×C₃	1	2	yes	complemented
126	C₂×#397	C₂×C₃	1	1	yes	characteristic, complemented
127	#2308	C₂×C₃	1	1	yes	characteristic, complemented
128	C₂⁵×C₃	C₂³	1	1	yes	characteristic
129	C₂⁵×C₃	C₂³	1	1	yes	characteristic
130	C₂×C₃×#41	—	2	8	no	—
131	C₂×C₃×#41	—	4	4	no	—
132	C₂×C₃×#41	—	4	4	no	—
133	C₂²×C₃×Q₈	C₂³	1	2	yes	—
134	C₂²×C₃×D₄	—	4	2	no	—
135	C₂²×C₃×D₄	—	4	2	no	—
136	C₂²×C₃×D₄	D₄	1	8	yes	complemented
137	C₂²×C₃×D₄	C₂³	1	2	yes	—
138	C₂²×C₃×D₄	C₂³	1	2	yes	—
139	C₂²×C₃×D₄	C₂³	1	2	yes	—
140	C₂²×C₃×D₄	C₂³	1	2	yes	—
141	C₂²×C₃×D₄	C₂³	1	2	yes	—
142	C₂²×C₃×D₄	C₂³	1	2	yes	—
143	C₂²×C₃×D₄	C₂³	1	1	yes	characteristic
144	C₂²×C₃×D₄	C₂³	1	2	yes	—
145	C₂³×C₃×C₄	C₂³	1	2	yes	—
146	C₂³×C₃×C₄	C₂³	1	2	yes	—
147	C₂³×C₃×C₄	C₂³	1	2	yes	—
148	C₂³×C₃×C₄	C₂³	1	1	yes	characteristic
149	C₂³×C₃×C₄	C₂³	1	2	yes	—
150	C₂³×C₃×C₄	C₂³	1	1	yes	characteristic
151	C₂³×C₃×C₄	C₂³	1	2	yes	—
152	C₂³×C₃×C₄	C₂³	1	2	yes	—
153	C₂³×C₃×C₄	C₂³	1	1	yes	characteristic
154	C₃×#124	—	2	8	no	—
155	C₃×#123	—	2	8	no	—
156	C₃×#123	—	2	8	no	—
157	C₃×#123	—	4	4	no	—
158	C₃×C₂²⋊Q₈	—	2	8	no	—
159	C₃×#121	—	2	8	no	—
160	C₃×#121	—	2	8	no	—
161	C₃×#121	—	2	8	no	—
162	C₃×#121	—	4	2	no	—
163	C₃×#120	—	2	8	no	—
164	C₃×#120	—	2	8	no	—
165	C₃×C₄×D₄	—	2	8	no	—
166	C₃×C₄×D₄	—	2	8	no	—
167	C₂×C₃×C₄⋊C₄	—	4	2	no	—
168	C₂×C₃×C₄⋊C₄	C₂³	1	2	yes	—
169	C₂×C₃×C₄⋊C₄	C₂³	1	2	yes	—
170	C₂×C₃×C₄⋊C₄	C₂³	1	2	yes	—
171	C₂×C₃×C₄⋊C₄	C₂³	1	2	yes	—
172	C₂×C₃×C₄⋊C₄	C₂³	1	2	yes	—
173	C₂×C₃×C₄⋊C₄	C₂³	1	2	yes	—
174	C₂×C₃×C₄⋊C₄	C₂³	1	2	yes	—
175	C₂×C₃×C₄⋊C₄	C₂³	1	2	yes	—
176	C₂×C₃×C₄⋊C₄	C₂³	1	2	yes	—
177	C₂×C₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
178	C₂×C₃×C₄⋊C₄	C₂³	1	2	yes	—
179	C₂×C₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
180	C₂×C₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
181	C₂×C₃×C₂²⋊C₄	—	2	8	no	—
182	C₂×C₃×C₂²⋊C₄	—	2	8	no	—
183	C₂×C₃×C₂²⋊C₄	—	4	2	no	—
184	C₂×C₃×C₂²⋊C₄	—	4	2	no	—
185	C₂×C₃×C₂²⋊C₄	C₂³	1	2	yes	—
186	C₂×C₃×C₂²⋊C₄	C₂³	1	2	yes	—
187	C₂×C₃×C₂²⋊C₄	C₂³	1	2	yes	—
188	C₂×C₃×C₂²⋊C₄	C₂³	1	2	yes	—
189	C₂×C₃×C₂²⋊C₄	C₂³	1	2	yes	—
190	C₂×C₃×C₂²⋊C₄	C₂³	1	2	yes	—
191	C₂×C₃×C₂²⋊C₄	C₂³	1	2	yes	—
192	C₂×C₃×C₂²⋊C₄	C₂³	1	2	yes	—
193	C₂×C₃×C₂²⋊C₄	C₂³	1	2	yes	—
194	C₂×C₃×C₂²⋊C₄	C₂³	1	2	yes	—
195	C₂×C₃×C₂²⋊C₄	C₂³	1	2	yes	—
196	C₂×C₃×C₂²⋊C₄	C₂³	1	2	yes	—
197	C₂×C₃×C₂²⋊C₄	C₂³	1	2	yes	—
198	C₂×C₃×C₂²⋊C₄	C₂³	1	1	yes	characteristic
199	C₂×C₃×C₂²⋊C₄	C₂³	1	1	yes	characteristic
200	C₂×C₃×C₂²⋊C₄	C₂³	1	1	yes	characteristic
201	C₂×C₃×C₂²⋊C₄	C₂³	1	1	yes	characteristic
202	C₂×C₃×C₂²⋊C₄	C₂³	1	2	yes	—
203	C₂×C₃×C₂²⋊C₄	C₂³	1	2	yes	—
204	C₂×C₃×C₂²⋊C₄	C₂³	1	2	yes	—
205	C₂×C₃×C₂²⋊C₄	C₂³	1	2	yes	—
206	C₂×C₃×C₂²⋊C₄	C₂³	1	2	yes	—
207	C₂×C₃×C₂²⋊C₄	C₂³	1	2	yes	—
208	C₂×C₃×C₂²⋊C₄	C₂³	1	2	yes	—
209	C₂×C₃×C₂²⋊C₄	C₂³	1	2	yes	—
210	C₂×C₃×C₂²⋊C₄	C₂³	1	2	yes	—
211	C₂×C₃×C₂²⋊C₄	C₂³	1	2	yes	—
212	C₂×C₃×C₂²⋊C₄	C₂³	1	1	yes	characteristic
213	C₂×C₃×C₂²⋊C₄	C₂³	1	1	yes	characteristic
214	C₂×C₃×C₂²⋊C₄	C₂³	1	2	yes	—
215	C₂×C₃×C₄²	C₂³	1	2	yes	—
216	C₃×#95	C₂³	1	1	yes	characteristic
217	C₃×#95	C₂³	1	2	yes	—
218	C₃×#95	C₂³	1	2	yes	—
219	C₃×#95	C₂³	1	2	yes	—
220	C₃×#95	C₂³	1	2	yes	—
221	C₃×#95	C₂³	1	2	yes	—
222	C₃×#95	C₂³	1	1	yes	characteristic
223	C₃×#95	C₂³	1	1	yes	characteristic
224	C₃×#95	C₂³	1	2	yes	—
225	C₃×#95	C₂³	1	2	yes	—
226	C₃×#95	C₂³	1	2	yes	—
227	C₃×#95	C₂³	1	2	yes	—
228	C₃×#95	C₂³	1	1	yes	characteristic
229	C₃×#95	C₂³	1	2	yes	—
230	C₃×#95	C₂³	1	2	yes	—
231	C₃×#95	C₂³	1	2	yes	—
232	C₃×#95	C₂³	1	2	yes	—
233	C₃×#95	C₂³	1	2	yes	—
234	C₃×#95	C₂³	1	2	yes	—
235	C₃×#95	C₂³	1	2	yes	—
236	C₃×#95	C₂³	1	2	yes	—
237	C₃×#95	C₂³	1	2	yes	—
238	C₃×#95	C₂³	1	2	yes	—
239	C₂²×#41	C₂²×C₃	1	2	yes	—
240	C₂³×D₄	C₂²×C₃	1	1	yes	characteristic
241	#546	—	2	16	no	—
242	C₂×#124	C₂²×C₃	1	2	yes	—
243	C₂×#123	C₂²×C₃	1	2	yes	—
244	C₂×#123	C₂²×C₃	1	2	yes	—
245	C₂×#123	C₂²×C₃	1	2	yes	complemented
246	C₂×C₂²⋊Q₈	C₂²×C₃	1	2	yes	—
247	C₂×#121	C₂²×C₃	1	2	yes	—
248	C₂×#121	C₂²×C₃	1	2	yes	—
249	C₂×#121	C₂²×C₃	1	2	yes	—
250	C₂×#121	C₂²×C₃	1	1	yes	characteristic, complemented
251	C₂×#120	C₂²×C₃	1	2	yes	—
252	C₂×#120	C₂²×C₃	1	2	yes	—
253	C₂×C₄×D₄	C₂²×C₃	1	2	yes	—
254	C₂×C₄×D₄	C₂²×C₃	1	2	yes	—
255	C₂²×C₄⋊C₄	C₂²×C₃	1	1	yes	characteristic, complemented
256	C₂²×C₂²⋊C₄	C₂²×C₃	1	2	yes	—
257	C₂²×C₂²⋊C₄	C₂²×C₃	1	2	yes	—
258	C₂²×C₂²⋊C₄	C₂²×C₃	1	1	yes	characteristic
259	C₂²×C₂²⋊C₄	C₂²×C₃	1	1	yes	characteristic
260	#400	C₂²×C₃	1	2	yes	complemented
261	#400	C₂²×C₃	1	2	yes	complemented
262	#398	C₂²×C₃	1	2	yes	complemented
263	#397	C₂²×C₃	1	1	yes	characteristic
264	#397	C₂²×C₃	1	2	yes	—
265	#397	C₂²×C₃	1	1	yes	characteristic
266	#397	C₂²×C₃	1	1	yes	characteristic
267	#397	C₂²×C₃	1	2	yes	—
268	#397	C₂²×C₃	1	2	yes	—
269	#397	C₂²×C₃	1	1	yes	characteristic, complemented
270	#397	C₂²×C₃	1	2	yes	complemented
271	#397	C₂²×C₃	1	2	yes	complemented
272	#397	C₂²×C₃	1	2	yes	complemented
273	#397	C₂²×C₃	1	1	yes	characteristic, complemented
274	#397	C₂²×C₃	1	2	yes	complemented
275	#397	C₂²×C₃	1	1	yes	characteristic, complemented
276	#397	C₂²×C₃	1	2	yes	complemented
277	#395	C₂²×C₃	1	2	yes	complemented
278	#395	C₂²×C₃	1	2	yes	complemented
279	#395	C₂²×C₃	1	2	yes	complemented
280	#394	C₂²×C₃	1	2	yes	—
281	#394	C₂²×C₃	1	2	yes	—
282	#394	C₂²×C₃	1	2	yes	—
283	#394	C₂²×C₃	1	2	yes	complemented
284	#394	C₂²×C₃	1	2	yes	complemented
285	#394	C₂²×C₃	1	2	yes	complemented
286	#394	C₂²×C₃	1	2	yes	complemented
287	#394	C₂²×C₃	1	2	yes	complemented
288	#393	C₂²×C₃	1	2	yes	complemented
289	#392	C₂²×C₃	1	1	yes	characteristic
290	#392	C₂²×C₃	1	1	yes	characteristic, complemented
291	#392	C₂²×C₃	1	2	yes	complemented
292	#388	C₂²×C₃	1	2	yes	complemented
293	#387	C₂²×C₃	1	2	yes	complemented
294	#387	C₂²×C₃	1	2	yes	complemented
295	#387	C₂²×C₃	1	2	yes	complemented
296	#386	C₂²×C₃	1	2	yes	—
297	#386	C₂²×C₃	1	2	yes	—
298	#386	C₂²×C₃	1	2	yes	—
299	#386	C₂²×C₃	1	2	yes	—
300	#386	C₂²×C₃	1	2	yes	complemented
301	#386	C₂²×C₃	1	2	yes	complemented
302	#386	C₂²×C₃	1	2	yes	complemented
303	#386	C₂²×C₃	1	2	yes	complemented
304	#386	C₂²×C₃	1	2	yes	complemented
305	#386	C₂²×C₃	1	2	yes	complemented
306	#386	C₂²×C₃	1	2	yes	complemented
307	#385	C₂²×C₃	1	2	yes	complemented
308	#385	C₂²×C₃	1	2	yes	complemented
309	#385	C₂²×C₃	1	2	yes	complemented
310	#385	C₂²×C₃	1	2	yes	complemented
311	#385	C₂²×C₃	1	2	yes	complemented
312	#385	C₂²×C₃	1	2	yes	complemented
313	#385	C₂²×C₃	1	2	yes	complemented
314	#385	C₂²×C₃	1	2	yes	complemented
315	#381	C₂²×C₃	1	1	yes	characteristic
316	#381	C₂²×C₃	1	1	yes	characteristic
317	#381	C₂²×C₃	1	2	yes	complemented
318	#381	C₂²×C₃	1	2	yes	complemented
319	#381	C₂²×C₃	1	2	yes	complemented
320	#380	C₂²×C₃	1	1	yes	characteristic, complemented
321	#380	C₂²×C₃	1	2	yes	complemented
322	#380	C₂²×C₃	1	2	yes	complemented
323	#379	C₂²×C₃	1	1	yes	characteristic
324	#379	C₂²×C₃	1	1	yes	characteristic
325	C₂×#95	C₂²×C₃	1	2	yes	complemented
326	C₂×#95	C₂²×C₃	1	1	yes	characteristic, complemented
327	C₂⁴×C₃	—	2	2	no	—
328	C₂⁴×C₃	—	2	2	no	—
329	C₂⁴×C₃	—	4	2	no	—
330	C₂⁴×C₃	—	4	2	no	—
331	C₂⁴×C₃	—	4	2	no	—
332	C₂⁴×C₃	—	4	2	no	—
333	C₂⁴×C₃	—	4	1	no	—
334	C₂⁴×C₃	—	4	1	no	—
335	C₂⁴×C₃	C₂×D₄	1	4	yes	—
336	C₂⁴×C₃	C₂×D₄	1	4	yes	—
337	C₂⁴×C₃	C₂⁴	1	2	yes	—
338	C₂⁴×C₃	C₂⁴	1	1	yes	characteristic
339	C₂⁴×C₃	C₂⁴	1	1	yes	characteristic
340	C₂⁴×C₃	C₂⁴	1	2	yes	—
341	C₂⁴×C₃	C₂⁴	1	1	yes	characteristic
342	C₃×#41	—	4	32	no	—
343	C₂×C₃×Q₈	—	2	4	no	—
344	C₂×C₃×Q₈	—	4	2	no	—
345	C₂×C₃×Q₈	—	4	2	no	—
346	C₂×C₃×D₄	—	2	4	no	—
347	C₂×C₃×D₄	—	2	4	no	—
348	C₂×C₃×D₄	—	2	4	no	—
349	C₂×C₃×D₄	—	2	4	no	—
350	C₂×C₃×D₄	—	2	4	no	—
351	C₂×C₃×D₄	—	2	4	no	—
352	C₂×C₃×D₄	—	2	4	no	—
353	C₂×C₃×D₄	—	2	4	no	—
354	C₂×C₃×D₄	—	2	4	no	—
355	C₂×C₃×D₄	—	4	2	no	—
356	C₂×C₃×D₄	—	4	2	no	—
357	C₂×C₃×D₄	—	4	2	no	—
358	C₂×C₃×D₄	—	4	2	no	—
359	C₂×C₃×D₄	—	4	2	no	—
360	C₂×C₃×D₄	—	4	2	no	—
361	C₂×C₃×D₄	—	4	1	no	—
362	C₂×C₃×D₄	—	4	2	no	—
363	C₂×C₃×D₄	—	4	2	no	—
364	C₂×C₃×D₄	—	4	2	no	—
365	C₂×C₃×D₄	—	4	2	no	—
366	C₂×C₃×D₄	—	4	2	no	—
367	C₂×C₃×D₄	—	4	16	no	—
368	C₂×C₃×D₄	C₂×D₄	1	8	yes	—
369	C₂×C₃×D₄	C₂×D₄	1	8	yes	—
370	C₂²×C₃×C₄	—	2	4	no	—
371	C₂²×C₃×C₄	—	2	4	no	—
372	C₂²×C₃×C₄	—	2	2	no	—
373	C₂²×C₃×C₄	—	2	4	no	—
374	C₂²×C₃×C₄	—	2	4	no	—
375	C₂²×C₃×C₄	—	2	4	no	—
376	C₂²×C₃×C₄	—	2	4	no	—
377	C₂²×C₃×C₄	—	2	2	no	—
378	C₂²×C₃×C₄	—	2	4	no	—
379	C₂²×C₃×C₄	—	4	2	no	—
380	C₂²×C₃×C₄	—	4	1	no	—
381	C₂²×C₃×C₄	—	4	1	no	—
382	C₂²×C₃×C₄	—	4	2	no	—
383	C₂²×C₃×C₄	—	4	2	no	—
384	C₂²×C₃×C₄	—	4	2	no	—
385	C₂²×C₃×C₄	—	4	2	no	—
386	C₂²×C₃×C₄	—	4	2	no	—
387	C₂²×C₃×C₄	—	4	2	no	—
388	C₂²×C₃×C₄	—	4	2	no	—
389	C₂²×C₃×C₄	—	4	2	no	—
390	C₂²×C₃×C₄	—	4	2	no	—
391	C₂²×C₃×C₄	—	4	2	no	—
392	C₂²×C₃×C₄	—	4	2	no	—
393	C₂²×C₃×C₄	—	4	2	no	—
394	C₂²×C₃×C₄	C₂×D₄	1	4	yes	—
395	C₂²×C₃×C₄	C₂⁴	1	1	yes	characteristic
396	C₂²×C₃×C₄	C₂⁴	1	2	yes	—
397	C₂²×C₃×C₄	C₂⁴	1	2	yes	—
398	C₂²×C₃×C₄	C₂⁴	1	2	yes	—
399	C₂²×C₃×C₄	C₂⁴	1	1	yes	characteristic
400	C₂²×C₃×C₄	C₂⁴	1	1	yes	characteristic
401	C₂²×C₃×C₄	C₂⁴	1	1	yes	characteristic
402	C₂²×C₃×C₄	C₂⁴	1	2	yes	—
403	C₂²×C₃×C₄	C₂⁴	1	2	yes	—
404	C₂²×C₃×C₄	C₂⁴	1	2	yes	—
405	C₂²×C₃×C₄	C₂⁴	1	2	yes	—
406	C₂²×C₃×C₄	C₂⁴	1	2	yes	—
407	C₂²×C₃×C₄	C₂⁴	1	2	yes	—
408	C₂²×C₃×C₄	C₂⁴	1	2	yes	—
409	C₃×C₄⋊C₄	—	2	4	no	—
410	C₃×C₄⋊C₄	—	2	4	no	—
411	C₃×C₄⋊C₄	—	2	4	no	—
412	C₃×C₄⋊C₄	—	2	4	no	—
413	C₃×C₄⋊C₄	—	4	1	no	—
414	C₃×C₄⋊C₄	—	4	2	no	—
415	C₃×C₄⋊C₄	—	4	1	no	—
416	C₃×C₄⋊C₄	—	4	2	no	—
417	C₃×C₄⋊C₄	—	4	2	no	—
418	C₃×C₄⋊C₄	—	4	2	no	—
419	C₃×C₄⋊C₄	—	4	1	no	—
420	C₃×C₄⋊C₄	—	4	2	no	—
421	C₃×C₄⋊C₄	—	4	2	no	—
422	C₃×C₂²⋊C₄	—	2	4	no	—
423	C₃×C₂²⋊C₄	—	2	4	no	—
424	C₃×C₂²⋊C₄	—	2	4	no	—
425	C₃×C₂²⋊C₄	—	2	4	no	—
426	C₃×C₂²⋊C₄	—	2	4	no	—
427	C₃×C₂²⋊C₄	—	2	4	no	—
428	C₃×C₂²⋊C₄	—	2	4	no	—
429	C₃×C₂²⋊C₄	—	2	4	no	—
430	C₃×C₂²⋊C₄	—	2	4	no	—
431	C₃×C₂²⋊C₄	—	2	4	no	—
432	C₃×C₂²⋊C₄	—	2	4	no	—
433	C₃×C₂²⋊C₄	—	2	4	no	—
434	C₃×C₂²⋊C₄	—	2	4	no	—
435	C₃×C₂²⋊C₄	—	4	1	no	—
436	C₃×C₂²⋊C₄	—	4	1	no	—
437	C₃×C₂²⋊C₄	—	4	1	no	—
438	C₃×C₂²⋊C₄	—	4	1	no	—
439	C₃×C₂²⋊C₄	—	4	1	no	—
440	C₃×C₂²⋊C₄	—	4	1	no	—
441	C₃×C₂²⋊C₄	—	4	2	no	—
442	C₃×C₂²⋊C₄	—	4	2	no	—
443	C₃×C₂²⋊C₄	—	4	2	no	—
444	C₃×C₂²⋊C₄	—	4	2	no	—
445	C₃×C₂²⋊C₄	—	4	2	no	—
446	C₃×C₂²⋊C₄	—	4	2	no	—
447	C₃×C₂²⋊C₄	—	4	2	no	—
448	C₃×C₂²⋊C₄	—	4	2	no	—
449	C₃×C₂²⋊C₄	—	4	2	no	—
450	C₃×C₂²⋊C₄	—	4	2	no	—
451	C₃×C₂²⋊C₄	—	4	2	no	—
452	C₃×C₄²	—	2	4	no	—
453	C₂⁵	C₂³×C₃	1	1	yes	characteristic
454	C₂⁵	C₂³×C₃	1	1	yes	characteristic
455	C₂×#41	—	2	8	no	—
456	C₂×#41	—	4	4	no	—
457	C₂×#41	—	4	4	no	—
458	C₂²×Q₈	C₂³×C₃	1	2	yes	—
459	C₂²×D₄	—	4	2	no	—
460	C₂²×D₄	—	4	2	no	—
461	C₂²×D₄	C₃×D₄	1	8	yes	complemented
462	C₂²×D₄	C₂³×C₃	1	2	yes	—
463	C₂²×D₄	C₂³×C₃	1	2	yes	—
464	C₂²×D₄	C₂³×C₃	1	2	yes	—
465	C₂²×D₄	C₂³×C₃	1	2	yes	—
466	C₂²×D₄	C₂³×C₃	1	2	yes	—
467	C₂²×D₄	C₂³×C₃	1	2	yes	—
468	C₂²×D₄	C₂³×C₃	1	1	yes	characteristic
469	C₂²×D₄	C₂³×C₃	1	2	yes	—
470	C₂³×C₄	C₂³×C₃	1	2	yes	—
471	C₂³×C₄	C₂³×C₃	1	1	yes	characteristic
472	C₂³×C₄	C₂³×C₃	1	2	yes	—
473	C₂³×C₄	C₂³×C₃	1	2	yes	—
474	C₂³×C₄	C₂³×C₃	1	1	yes	characteristic
475	C₂³×C₄	C₂³×C₃	1	2	yes	—
476	C₂³×C₄	C₂³×C₃	1	2	yes	—
477	C₂³×C₄	C₂³×C₃	1	2	yes	—
478	C₂³×C₄	C₂³×C₃	1	1	yes	characteristic
479	#124	—	2	8	no	—
480	#123	—	2	8	no	—
481	#123	—	2	8	no	—
482	#123	—	4	4	no	—
483	C₂²⋊Q₈	—	2	8	no	—
484	#121	—	2	8	no	—
485	#121	—	2	8	no	—
486	#121	—	2	8	no	—
487	#121	—	4	2	no	—
488	#120	—	2	8	no	—
489	#120	—	2	8	no	—
490	C₄×D₄	—	2	8	no	—
491	C₄×D₄	—	2	8	no	—
492	C₂×C₄⋊C₄	—	4	2	no	—
493	C₂×C₄⋊C₄	C₂³×C₃	1	2	yes	—
494	C₂×C₄⋊C₄	C₂³×C₃	1	2	yes	—
495	C₂×C₄⋊C₄	C₂³×C₃	1	2	yes	—
496	C₂×C₄⋊C₄	C₂³×C₃	1	2	yes	—
497	C₂×C₄⋊C₄	C₂³×C₃	1	1	yes	characteristic
498	C₂×C₄⋊C₄	C₂³×C₃	1	2	yes	—
499	C₂×C₄⋊C₄	C₂³×C₃	1	1	yes	characteristic
500	C₂×C₄⋊C₄	C₂³×C₃	1	1	yes	characteristic
501	C₂×C₄⋊C₄	C₂³×C₃	1	2	yes	—
502	C₂×C₄⋊C₄	C₂³×C₃	1	2	yes	—
503	C₂×C₄⋊C₄	C₂³×C₃	1	2	yes	—
504	C₂×C₄⋊C₄	C₂³×C₃	1	2	yes	—
505	C₂×C₄⋊C₄	C₂³×C₃	1	2	yes	—
506	C₂×C₂²⋊C₄	—	2	8	no	—
507	C₂×C₂²⋊C₄	—	2	8	no	—
508	C₂×C₂²⋊C₄	—	4	2	no	—
509	C₂×C₂²⋊C₄	—	4	2	no	—
510	C₂×C₂²⋊C₄	C₂³×C₃	1	2	yes	—
511	C₂×C₂²⋊C₄	C₂³×C₃	1	2	yes	—
512	C₂×C₂²⋊C₄	C₂³×C₃	1	2	yes	—
513	C₂×C₂²⋊C₄	C₂³×C₃	1	2	yes	—
514	C₂×C₂²⋊C₄	C₂³×C₃	1	2	yes	—
515	C₂×C₂²⋊C₄	C₂³×C₃	1	2	yes	—
516	C₂×C₂²⋊C₄	C₂³×C₃	1	2	yes	—
517	C₂×C₂²⋊C₄	C₂³×C₃	1	2	yes	—
518	C₂×C₂²⋊C₄	C₂³×C₃	1	2	yes	—
519	C₂×C₂²⋊C₄	C₂³×C₃	1	2	yes	—
520	C₂×C₂²⋊C₄	C₂³×C₃	1	2	yes	—
521	C₂×C₂²⋊C₄	C₂³×C₃	1	2	yes	—
522	C₂×C₂²⋊C₄	C₂³×C₃	1	2	yes	—
523	C₂×C₂²⋊C₄	C₂³×C₃	1	1	yes	characteristic
524	C₂×C₂²⋊C₄	C₂³×C₃	1	1	yes	characteristic
525	C₂×C₂²⋊C₄	C₂³×C₃	1	1	yes	characteristic
526	C₂×C₂²⋊C₄	C₂³×C₃	1	1	yes	characteristic
527	C₂×C₂²⋊C₄	C₂³×C₃	1	1	yes	characteristic
528	C₂×C₂²⋊C₄	C₂³×C₃	1	1	yes	characteristic
529	C₂×C₂²⋊C₄	C₂³×C₃	1	2	yes	—
530	C₂×C₂²⋊C₄	C₂³×C₃	1	2	yes	—
531	C₂×C₂²⋊C₄	C₂³×C₃	1	2	yes	—
532	C₂×C₂²⋊C₄	C₂³×C₃	1	2	yes	—
533	C₂×C₂²⋊C₄	C₂³×C₃	1	2	yes	—
534	C₂×C₂²⋊C₄	C₂³×C₃	1	2	yes	—
535	C₂×C₂²⋊C₄	C₂³×C₃	1	2	yes	—
536	C₂×C₂²⋊C₄	C₂³×C₃	1	2	yes	—
537	C₂×C₂²⋊C₄	C₂³×C₃	1	2	yes	—
538	C₂×C₂²⋊C₄	C₂³×C₃	1	2	yes	—
539	C₂×C₂²⋊C₄	C₂³×C₃	1	2	yes	—
540	C₂×C₄²	C₂³×C₃	1	2	yes	—
541	#95	C₂³×C₃	1	1	yes	characteristic
542	#95	C₂³×C₃	1	2	yes	—
543	#95	C₂³×C₃	1	2	yes	—
544	#95	C₂³×C₃	1	2	yes	—
545	#95	C₂³×C₃	1	2	yes	—
546	#95	C₂³×C₃	1	2	yes	—
547	#95	C₂³×C₃	1	1	yes	characteristic
548	#95	C₂³×C₃	1	1	yes	characteristic
549	#95	C₂³×C₃	1	2	yes	—
550	#95	C₂³×C₃	1	2	yes	—
551	#95	C₂³×C₃	1	2	yes	—
552	#95	C₂³×C₃	1	2	yes	—
553	#95	C₂³×C₃	1	1	yes	characteristic
554	#95	C₂³×C₃	1	2	yes	—
555	#95	C₂³×C₃	1	2	yes	—
556	#95	C₂³×C₃	1	2	yes	—
557	#95	C₂³×C₃	1	2	yes	—
558	#95	C₂³×C₃	1	2	yes	—
559	#95	C₂³×C₃	1	2	yes	—
560	#95	C₂³×C₃	1	2	yes	—
561	#95	C₂³×C₃	1	2	yes	—
562	#95	C₂³×C₃	1	2	yes	—
563	#95	C₂³×C₃	1	2	yes	—
564	C₂³×C₃	—	2	2	no	—
565	C₂³×C₃	—	2	2	no	—
566	C₂³×C₃	—	2	1	no	—
567	C₂³×C₃	—	2	1	no	—
568	C₂³×C₃	—	2	1	no	—
569	C₂³×C₃	—	2	1	no	—
570	C₂³×C₃	—	2	2	no	—
571	C₂³×C₃	—	2	2	no	—
572	C₂³×C₃	—	2	2	no	—
573	C₂³×C₃	—	2	2	no	—
574	C₂³×C₃	—	2	2	no	—
575	C₂³×C₃	—	2	2	no	—
576	C₂³×C₃	—	2	2	no	—
577	C₂³×C₃	—	2	2	no	—
578	C₂³×C₃	—	2	2	no	—
579	C₂³×C₃	—	2	2	no	—
580	C₂³×C₃	—	2	8	no	—
581	C₂³×C₃	—	2	2	no	—
582	C₂³×C₃	—	2	2	no	—
583	C₂³×C₃	—	2	2	no	—
584	C₂³×C₃	—	2	2	no	—
585	C₂³×C₃	—	2	2	no	—
586	C₂³×C₃	—	2	2	no	—
587	C₂³×C₃	—	2	2	no	—
588	C₂³×C₃	—	4	4	no	—
589	C₂³×C₃	—	4	8	no	—
590	C₂³×C₃	—	4	8	no	—
591	C₂³×C₃	—	8	2	no	—
592	C₂³×C₃	—	8	2	no	—
593	C₂³×C₃	—	8	4	no	—
594	C₂³×C₃	—	8	2	no	—
595	C₂³×C₃	—	8	2	no	—
596	C₂³×C₃	—	8	4	no	—
597	C₂³×C₃	C₂²×D₄	1	2	yes	—
598	C₂³×C₃	C₂²×D₄	1	2	yes	—
599	C₂³×C₃	C₂²×D₄	1	4	yes	—
600	C₂³×C₃	C₂²×D₄	1	2	yes	—
601	C₂³×C₃	H(5,𝔽₂)	1	2	yes	—
602	C₂³×C₃	H(5,𝔽₂)	1	2	yes	—
603	C₂³×C₃	C₂⁵	1	1	yes	characteristic
604	C₃×Q₈	—	4	8	no	—
605	C₃×D₄	—	2	16	no	—
606	C₃×D₄	—	4	8	no	—
607	C₃×D₄	—	4	8	no	—
608	C₃×D₄	—	4	8	no	—
609	C₃×D₄	—	4	8	no	—
610	C₃×D₄	—	8	4	no	—
611	C₃×D₄	—	8	4	no	—
612	C₃×D₄	—	8	2	no	—
613	C₂×C₃×C₄	—	2	2	no	—
614	C₂×C₃×C₄	—	2	2	no	—
615	C₂×C₃×C₄	—	2	2	no	—
616	C₂×C₃×C₄	—	2	2	no	—
617	C₂×C₃×C₄	—	2	2	no	—
618	C₂×C₃×C₄	—	2	2	no	—
619	C₂×C₃×C₄	—	2	2	no	—
620	C₂×C₃×C₄	—	2	2	no	—
621	C₂×C₃×C₄	—	2	2	no	—
622	C₂×C₃×C₄	—	2	2	no	—
623	C₂×C₃×C₄	—	2	2	no	—
624	C₂×C₃×C₄	—	2	1	no	—
625	C₂×C₃×C₄	—	2	1	no	—
626	C₂×C₃×C₄	—	2	1	no	—
627	C₂×C₃×C₄	—	2	1	no	—
628	C₂×C₃×C₄	—	2	2	no	—
629	C₂×C₃×C₄	—	2	2	no	—
630	C₂×C₃×C₄	—	2	2	no	—
631	C₂×C₃×C₄	—	2	2	no	—
632	C₂×C₃×C₄	—	2	2	no	—
633	C₂×C₃×C₄	—	2	2	no	—
634	C₂×C₃×C₄	—	2	2	no	—
635	C₂×C₃×C₄	—	2	2	no	—
636	C₂×C₃×C₄	—	2	2	no	—
637	C₂×C₃×C₄	—	2	2	no	—
638	C₂×C₃×C₄	—	2	2	no	—
639	C₂×C₃×C₄	—	2	2	no	—
640	C₂×C₃×C₄	—	2	2	no	—
641	C₂×C₃×C₄	—	2	2	no	—
642	C₂×C₃×C₄	—	2	2	no	—
643	C₂×C₃×C₄	—	2	2	no	—
644	C₂×C₃×C₄	—	2	2	no	—
645	C₂×C₃×C₄	—	2	2	no	—
646	C₂×C₃×C₄	—	2	2	no	—
647	C₂×C₃×C₄	—	2	2	no	—
648	C₂×C₃×C₄	—	2	2	no	—
649	C₂×C₃×C₄	—	2	2	no	—
650	C₂×C₃×C₄	—	4	4	no	—
651	C₂×C₃×C₄	—	4	8	no	—
652	C₂×C₃×C₄	—	4	4	no	—
653	C₂×C₃×C₄	—	4	8	no	—
654	C₂×C₃×C₄	—	4	8	no	—
655	C₂×C₃×C₄	—	8	4	no	—
656	C₂×C₃×C₄	—	8	4	no	—
657	C₂×C₃×C₄	—	8	2	no	—
658	C₂×C₃×C₄	—	8	4	no	—
659	C₂×C₃×C₄	C₂²×D₄	1	4	yes	—
660	C₂⁴	—	2	2	no	—
661	C₂⁴	—	2	2	no	—
662	C₂⁴	—	4	1	no	—
663	C₂⁴	—	4	1	no	—
664	C₂⁴	—	4	2	no	—
665	C₂⁴	—	4	2	no	—
666	C₂⁴	—	4	2	no	—
667	C₂⁴	—	4	2	no	—
668	C₂⁴	C₂×C₃×D₄	1	4	yes	—
669	C₂⁴	C₂×C₃×D₄	1	4	yes	—
670	C₂⁴	C₂⁴×C₃	1	2	yes	—
671	C₂⁴	C₂⁴×C₃	1	1	yes	characteristic
672	C₂⁴	C₂⁴×C₃	1	1	yes	characteristic
673	C₂⁴	C₂⁴×C₃	1	2	yes	—
674	C₂⁴	C₂⁴×C₃	1	1	yes	characteristic
675	#41	—	4	32	no	—
676	C₂×Q₈	—	2	4	no	—
677	C₂×Q₈	—	4	2	no	—
678	C₂×Q₈	—	4	2	no	—
679	C₂×D₄	—	2	4	no	—
680	C₂×D₄	—	2	4	no	—
681	C₂×D₄	—	2	4	no	—
682	C₂×D₄	—	2	4	no	—
683	C₂×D₄	—	2	4	no	—
684	C₂×D₄	—	2	4	no	—
685	C₂×D₄	—	2	4	no	—
686	C₂×D₄	—	2	4	no	—
687	C₂×D₄	—	2	4	no	—
688	C₂×D₄	—	4	2	no	—
689	C₂×D₄	—	4	2	no	—
690	C₂×D₄	—	4	2	no	—
691	C₂×D₄	—	4	2	no	—
692	C₂×D₄	—	4	2	no	—
693	C₂×D₄	—	4	2	no	—
694	C₂×D₄	—	4	1	no	—
695	C₂×D₄	—	4	2	no	—
696	C₂×D₄	—	4	2	no	—
697	C₂×D₄	—	4	2	no	—
698	C₂×D₄	—	4	2	no	—
699	C₂×D₄	—	4	2	no	—
700	C₂×D₄	—	4	16	no	—
701	C₂×D₄	C₂×C₃×D₄	1	8	yes	—
702	C₂×D₄	C₂×C₃×D₄	1	8	yes	—
703	C₂²×C₄	—	2	4	no	—
704	C₂²×C₄	—	2	4	no	—
705	C₂²×C₄	—	2	2	no	—
706	C₂²×C₄	—	2	4	no	—
707	C₂²×C₄	—	2	4	no	—
708	C₂²×C₄	—	2	4	no	—
709	C₂²×C₄	—	2	4	no	—
710	C₂²×C₄	—	2	2	no	—
711	C₂²×C₄	—	2	4	no	—
712	C₂²×C₄	—	4	1	no	—
713	C₂²×C₄	—	4	1	no	—
714	C₂²×C₄	—	4	2	no	—
715	C₂²×C₄	—	4	2	no	—
716	C₂²×C₄	—	4	2	no	—
717	C₂²×C₄	—	4	2	no	—
718	C₂²×C₄	—	4	2	no	—
719	C₂²×C₄	—	4	2	no	—
720	C₂²×C₄	—	4	2	no	—
721	C₂²×C₄	—	4	2	no	—
722	C₂²×C₄	—	4	2	no	—
723	C₂²×C₄	—	4	2	no	—
724	C₂²×C₄	—	4	2	no	—
725	C₂²×C₄	—	4	2	no	—
726	C₂²×C₄	—	4	2	no	—
727	C₂²×C₄	C₂×C₃×D₄	1	4	yes	—
728	C₂²×C₄	C₂⁴×C₃	1	1	yes	characteristic
729	C₂²×C₄	C₂⁴×C₃	1	2	yes	—
730	C₂²×C₄	C₂⁴×C₃	1	2	yes	—
731	C₂²×C₄	C₂⁴×C₃	1	2	yes	—
732	C₂²×C₄	C₂⁴×C₃	1	1	yes	characteristic
733	C₂²×C₄	C₂⁴×C₃	1	1	yes	characteristic
734	C₂²×C₄	C₂⁴×C₃	1	1	yes	characteristic
735	C₂²×C₄	C₂⁴×C₃	1	2	yes	—
736	C₂²×C₄	C₂⁴×C₃	1	2	yes	—
737	C₂²×C₄	C₂⁴×C₃	1	2	yes	—
738	C₂²×C₄	C₂⁴×C₃	1	2	yes	—
739	C₂²×C₄	C₂⁴×C₃	1	2	yes	—
740	C₂²×C₄	C₂⁴×C₃	1	2	yes	—
741	C₂²×C₄	C₂⁴×C₃	1	2	yes	—
742	C₄⋊C₄	—	2	4	no	—
743	C₄⋊C₄	—	2	4	no	—
744	C₄⋊C₄	—	2	4	no	—
745	C₄⋊C₄	—	2	4	no	—
746	C₄⋊C₄	—	4	1	no	—
747	C₄⋊C₄	—	4	2	no	—
748	C₄⋊C₄	—	4	1	no	—
749	C₄⋊C₄	—	4	1	no	—
750	C₄⋊C₄	—	4	2	no	—
751	C₄⋊C₄	—	4	2	no	—
752	C₄⋊C₄	—	4	2	no	—
753	C₄⋊C₄	—	4	2	no	—
754	C₄⋊C₄	—	4	2	no	—
755	C₂²⋊C₄	—	2	4	no	—
756	C₂²⋊C₄	—	2	4	no	—
757	C₂²⋊C₄	—	2	4	no	—
758	C₂²⋊C₄	—	2	4	no	—
759	C₂²⋊C₄	—	2	4	no	—
760	C₂²⋊C₄	—	2	4	no	—
761	C₂²⋊C₄	—	2	4	no	—
762	C₂²⋊C₄	—	2	4	no	—
763	C₂²⋊C₄	—	2	4	no	—
764	C₂²⋊C₄	—	2	4	no	—
765	C₂²⋊C₄	—	2	4	no	—
766	C₂²⋊C₄	—	2	4	no	—
767	C₂²⋊C₄	—	2	4	no	—
768	C₂²⋊C₄	—	4	1	no	—
769	C₂²⋊C₄	—	4	1	no	—
770	C₂²⋊C₄	—	4	1	no	—
771	C₂²⋊C₄	—	4	1	no	—
772	C₂²⋊C₄	—	4	1	no	—
773	C₂²⋊C₄	—	4	1	no	—
774	C₂²⋊C₄	—	4	2	no	—
775	C₂²⋊C₄	—	4	2	no	—
776	C₂²⋊C₄	—	4	2	no	—
777	C₂²⋊C₄	—	4	2	no	—
778	C₂²⋊C₄	—	4	2	no	—
779	C₂²⋊C₄	—	4	2	no	—
780	C₂²⋊C₄	—	4	2	no	—
781	C₂²⋊C₄	—	4	2	no	—
782	C₂²⋊C₄	—	4	2	no	—
783	C₂²⋊C₄	—	4	2	no	—
784	C₂²⋊C₄	—	4	2	no	—
785	C₄²	—	2	4	no	—
786	C₂²×C₃	—	2	4	no	—
787	C₂²×C₃	—	2	2	no	—
788	C₂²×C₃	—	2	2	no	—
789	C₂²×C₃	—	2	4	no	—
790	C₂²×C₃	—	2	4	no	—
791	C₂²×C₃	—	2	2	no	—
792	C₂²×C₃	—	2	2	no	—
793	C₂²×C₃	—	2	4	no	—
794	C₂²×C₃	—	2	4	no	—
795	C₂²×C₃	—	2	4	no	—
796	C₂²×C₃	—	2	4	no	—
797	C₂²×C₃	—	4	1	no	—
798	C₂²×C₃	—	4	2	no	—
799	C₂²×C₃	—	4	1	no	—
800	C₂²×C₃	—	4	1	no	—
801	C₂²×C₃	—	4	2	no	—
802	C₂²×C₃	—	4	1	no	—
803	C₂²×C₃	—	4	2	no	—
804	C₂²×C₃	—	4	2	no	—
805	C₂²×C₃	—	4	2	no	—
806	C₂²×C₃	—	4	2	no	—
807	C₂²×C₃	—	4	2	no	—
808	C₂²×C₃	—	4	2	no	—
809	C₂²×C₃	—	4	2	no	—
810	C₂²×C₃	—	4	2	no	—
811	C₂²×C₃	—	4	2	no	—
812	C₂²×C₃	—	4	2	no	—
813	C₂²×C₃	—	4	2	no	—
814	C₂²×C₃	—	8	8	no	—
815	C₂²×C₃	—	8	8	no	—
816	C₂²×C₃	#534	1	4	yes	—
817	C₂²×C₃	C₂³×D₄	1	1	yes	characteristic
818	C₂²×C₃	C₂×H(5,𝔽₂)	1	1	yes	characteristic
819	C₂²×C₃	C₂×H(5,𝔽₂)	1	1	yes	characteristic
820	C₂²×C₃	#585	1	2	yes	—
821	C₂²×C₃	#585	1	2	yes	—
822	C₃×C₄	—	2	4	no	—
823	C₃×C₄	—	4	2	no	—
824	C₃×C₄	—	4	2	no	—
825	C₃×C₄	—	4	2	no	—
826	C₃×C₄	—	4	2	no	—
827	C₃×C₄	—	4	2	no	—
828	C₃×C₄	—	4	2	no	—
829	C₃×C₄	—	4	2	no	—
830	C₃×C₄	—	4	1	no	—
831	C₃×C₄	—	4	1	no	—
832	C₃×C₄	—	4	1	no	—
833	C₃×C₄	—	4	1	no	—
834	C₃×C₄	—	4	2	no	—
835	C₃×C₄	—	4	2	no	—
836	C₂³	—	2	2	no	—
837	C₂³	—	2	2	no	—
838	C₂³	—	2	1	no	—
839	C₂³	—	2	1	no	—
840	C₂³	—	2	1	no	—
841	C₂³	—	2	1	no	—
842	C₂³	—	2	2	no	—
843	C₂³	—	2	2	no	—
844	C₂³	—	2	2	no	—
845	C₂³	—	2	2	no	—
846	C₂³	—	2	2	no	—
847	C₂³	—	2	2	no	—
848	C₂³	—	2	2	no	—
849	C₂³	—	2	2	no	—
850	C₂³	—	2	2	no	—
851	C₂³	—	2	2	no	—
852	C₂³	—	2	8	no	—
853	C₂³	—	2	2	no	—
854	C₂³	—	2	2	no	—
855	C₂³	—	2	2	no	—
856	C₂³	—	2	2	no	—
857	C₂³	—	2	2	no	—
858	C₂³	—	2	2	no	—
859	C₂³	—	2	2	no	—
860	C₂³	—	4	4	no	—
861	C₂³	—	4	8	no	—
862	C₂³	—	4	8	no	—
863	C₂³	—	8	2	no	—
864	C₂³	—	8	2	no	—
865	C₂³	—	8	4	no	—
866	C₂³	—	8	2	no	—
867	C₂³	—	8	2	no	—
868	C₂³	—	8	4	no	—
869	C₂³	C₂²×C₃×D₄	1	2	yes	—
870	C₂³	C₂²×C₃×D₄	1	2	yes	—
871	C₂³	C₂²×C₃×D₄	1	4	yes	—
872	C₂³	C₂²×C₃×D₄	1	2	yes	—
873	C₂³	C₃×H(5,𝔽₂)	1	2	yes	—
874	C₂³	C₃×H(5,𝔽₂)	1	2	yes	—
875	C₂³	C₂⁵×C₃	1	1	yes	characteristic
876	Q₈	—	4	8	no	—
877	D₄	—	2	16	no	—
878	D₄	—	4	8	no	—
879	D₄	—	4	8	no	—
880	D₄	—	4	8	no	—
881	D₄	—	4	8	no	—
882	D₄	—	8	4	no	—
883	D₄	—	8	4	no	—
884	D₄	—	8	2	no	—
885	C₂×C₄	—	2	2	no	—
886	C₂×C₄	—	2	2	no	—
887	C₂×C₄	—	2	2	no	—
888	C₂×C₄	—	2	2	no	—
889	C₂×C₄	—	2	2	no	—
890	C₂×C₄	—	2	2	no	—
891	C₂×C₄	—	2	2	no	—
892	C₂×C₄	—	2	2	no	—
893	C₂×C₄	—	2	2	no	—
894	C₂×C₄	—	2	2	no	—
895	C₂×C₄	—	2	2	no	—
896	C₂×C₄	—	2	1	no	—
897	C₂×C₄	—	2	1	no	—
898	C₂×C₄	—	2	1	no	—
899	C₂×C₄	—	2	1	no	—
900	C₂×C₄	—	2	2	no	—
901	C₂×C₄	—	2	2	no	—
902	C₂×C₄	—	2	2	no	—
903	C₂×C₄	—	2	2	no	—
904	C₂×C₄	—	2	2	no	—
905	C₂×C₄	—	2	2	no	—
906	C₂×C₄	—	2	2	no	—
907	C₂×C₄	—	2	2	no	—
908	C₂×C₄	—	2	2	no	—
909	C₂×C₄	—	2	2	no	—
910	C₂×C₄	—	2	2	no	—
911	C₂×C₄	—	2	2	no	—
912	C₂×C₄	—	2	2	no	—
913	C₂×C₄	—	2	2	no	—
914	C₂×C₄	—	2	2	no	—
915	C₂×C₄	—	2	2	no	—
916	C₂×C₄	—	2	2	no	—
917	C₂×C₄	—	2	2	no	—
918	C₂×C₄	—	2	2	no	—
919	C₂×C₄	—	2	2	no	—
920	C₂×C₄	—	2	2	no	—
921	C₂×C₄	—	2	2	no	—
922	C₂×C₄	—	4	4	no	—
923	C₂×C₄	—	4	8	no	—
924	C₂×C₄	—	4	8	no	—
925	C₂×C₄	—	4	4	no	—
926	C₂×C₄	—	4	8	no	—
927	C₂×C₄	—	8	4	no	—
928	C₂×C₄	—	8	4	no	—
929	C₂×C₄	—	8	2	no	—
930	C₂×C₄	—	8	4	no	—
931	C₂×C₄	C₂²×C₃×D₄	1	4	yes	—
932	C₂×C₃	—	2	4	no	—
933	C₂×C₃	—	4	4	no	—
934	C₂×C₃	—	4	2	no	—
935	C₂×C₃	—	4	2	no	—
936	C₂×C₃	—	8	2	no	—
937	C₂×C₃	C₂×#534	1	1	yes	characteristic
938	C₂×C₃	#3485	1	2	yes	—
939	C₂×C₃	#3533	1	1	yes	characteristic
940	C₂×C₃	#3545	1	1	yes	characteristic
941	C₂×C₃	#3560	1	2	yes	—
942	C₂²	—	2	4	no	—
943	C₂²	—	2	2	no	—
944	C₂²	—	2	2	no	—
945	C₂²	—	2	4	no	—
946	C₂²	—	2	4	no	—
947	C₂²	—	2	2	no	—
948	C₂²	—	2	2	no	—
949	C₂²	—	2	4	no	—
950	C₂²	—	2	4	no	—
951	C₂²	—	2	4	no	—
952	C₂²	—	2	4	no	—
953	C₂²	—	4	1	no	—
954	C₂²	—	4	1	no	—
955	C₂²	—	4	2	no	—
956	C₂²	—	4	1	no	—
957	C₂²	—	4	1	no	—
958	C₂²	—	4	2	no	—
959	C₂²	—	4	2	no	—
960	C₂²	—	4	2	no	—
961	C₂²	—	4	2	no	—
962	C₂²	—	4	2	no	—
963	C₂²	—	4	2	no	—
964	C₂²	—	4	2	no	—
965	C₂²	—	4	2	no	—
966	C₂²	—	4	2	no	—
967	C₂²	—	4	2	no	—
968	C₂²	—	4	2	no	—
969	C₂²	—	4	2	no	—
970	C₂²	—	8	8	no	—
971	C₂²	—	8	8	no	—
972	C₂²	C₃×#534	1	4	yes	—
973	C₂²	C₂³×C₃×D₄	1	1	yes	characteristic
974	C₂²	C₂×C₃×H(5,𝔽₂)	1	1	yes	characteristic
975	C₂²	C₂×C₃×H(5,𝔽₂)	1	1	yes	characteristic
976	C₂²	C₃×#585	1	2	yes	—
977	C₂²	C₃×#585	1	2	yes	—
978	C₄	—	2	4	no	—
979	C₄	—	4	2	no	—
980	C₄	—	4	2	no	—
981	C₄	—	4	2	no	—
982	C₄	—	4	2	no	—
983	C₄	—	4	2	no	—
984	C₄	—	4	2	no	—
985	C₄	—	4	2	no	—
986	C₄	—	4	1	no	—
987	C₄	—	4	1	no	—
988	C₄	—	4	1	no	—
989	C₄	—	4	1	no	—
990	C₄	—	4	2	no	—
991	C₄	—	4	2	no	—
992	C₃	#41404	1	1	yes	characteristic, direct product factor, Sylow
993	C₂	—	2	4	no	—
994	C₂	—	4	2	no	—
995	C₂	—	4	4	no	—
996	C₂	—	4	2	no	—
997	C₂	—	8	2	no	—
998	C₂	C₂×C₃×#534	1	1	yes	characteristic
999	C₂	C₃×#3485	1	2	yes	—
1000	C₂	C₃×#3533	1	1	yes	characteristic
1001	C₂	C₃×#3545	1	1	yes	characteristic
1002	C₂	C₃×#3560	1	2	yes	—

	subgroup	G/H
center, socle	C₂³×C₃	C₂⁵
commutator, Frattini, cosocle	C₂³	C₂⁵×C₃
LCS	G ▷ C₂³ ▷ C₁
UCS	C₁ ◁ C₂³×C₃ ◁ G

Complements

Splittings G = N ⋊ H with N normal; H ≅ G/N.

N	H ≅ G/N	type
1. C₂×C₃×#546	C₂	semidirect
2. C₃×#2817	C₂	semidirect
3. C₃×#2812	C₂	semidirect
4. C₃×#2717	C₂	semidirect
5. C₃×#2708	C₂	semidirect
6. C₃×#2688	C₂	semidirect
7. C₃×#2686	C₂	semidirect
8. C₃×#2638	C₂	semidirect
9. C₃×#2622	C₂	semidirect
10. C₃×#2617	C₂	semidirect
11. C₃×#2600	C₂	semidirect
12. C₃×#2483	C₂	semidirect
13. C₃×#2444	C₂	semidirect
14. C₃×#2430	C₂	semidirect
15. C₃×#2419	C₂	semidirect
16. C₃×#2412	C₂	semidirect
17. C₃×#2406	C₂	semidirect
18. C₂×C₃×#397	C₂	semidirect
19. C₃×#2308	C₂	semidirect
20. #41404	C₃	direct (N × H)
27. C₂×C₃×#123	C₂²	semidirect
32. C₂×C₃×#121	C₂²	semidirect
37. C₂²×C₃×C₄⋊C₄	C₂²	semidirect
42. C₃×#400	C₂²	semidirect
43. C₃×#400	C₂²	semidirect
44. C₃×#398	C₂²	semidirect
51. C₃×#397	C₂²	semidirect
52. C₃×#397	C₂²	semidirect
53. C₃×#397	C₂²	semidirect
54. C₃×#397	C₂²	semidirect
55. C₃×#397	C₂²	semidirect
56. C₃×#397	C₂²	semidirect
57. C₃×#397	C₂²	semidirect
58. C₃×#397	C₂²	semidirect
59. C₃×#395	C₂²	semidirect
60. C₃×#395	C₂²	semidirect
61. C₃×#395	C₂²	semidirect
65. C₃×#394	C₂²	semidirect
66. C₃×#394	C₂²	semidirect
67. C₃×#394	C₂²	semidirect
68. C₃×#394	C₂²	semidirect
69. C₃×#394	C₂²	semidirect
70. C₃×#393	C₂²	semidirect
72. C₃×#392	C₂²	semidirect
73. C₃×#392	C₂²	semidirect
74. C₃×#388	C₂²	semidirect
75. C₃×#387	C₂²	semidirect
76. C₃×#387	C₂²	semidirect
77. C₃×#387	C₂²	semidirect
82. C₃×#386	C₂²	semidirect
83. C₃×#386	C₂²	semidirect
84. C₃×#386	C₂²	semidirect
85. C₃×#386	C₂²	semidirect
86. C₃×#386	C₂²	semidirect
87. C₃×#386	C₂²	semidirect
88. C₃×#386	C₂²	semidirect
89. C₃×#385	C₂²	semidirect
90. C₃×#385	C₂²	semidirect
91. C₃×#385	C₂²	semidirect
92. C₃×#385	C₂²	semidirect
93. C₃×#385	C₂²	semidirect
94. C₃×#385	C₂²	semidirect
95. C₃×#385	C₂²	semidirect
96. C₃×#385	C₂²	semidirect
99. C₃×#381	C₂²	semidirect
100. C₃×#381	C₂²	semidirect
101. C₃×#381	C₂²	semidirect
102. C₃×#380	C₂²	semidirect
103. C₃×#380	C₂²	semidirect
104. C₃×#380	C₂²	semidirect
107. C₂×C₃×#95	C₂²	semidirect
108. C₂×C₃×#95	C₂²	semidirect
109. C₂×#546	C₂×C₃	semidirect
110. #2817	C₂×C₃	semidirect
111. #2812	C₂×C₃	semidirect
112. #2717	C₂×C₃	semidirect
113. #2708	C₂×C₃	semidirect
114. #2688	C₂×C₃	semidirect
115. #2686	C₂×C₃	semidirect
116. #2638	C₂×C₃	semidirect
117. #2622	C₂×C₃	semidirect
118. #2617	C₂×C₃	semidirect
119. #2600	C₂×C₃	semidirect
120. #2483	C₂×C₃	semidirect
121. #2444	C₂×C₃	semidirect
122. #2430	C₂×C₃	semidirect
123. #2419	C₂×C₃	semidirect
124. #2412	C₂×C₃	semidirect
125. #2406	C₂×C₃	semidirect
126. C₂×#397	C₂×C₃	semidirect
127. #2308	C₂×C₃	semidirect
136. C₂²×C₃×D₄	D₄	semidirect
245. C₂×#123	C₂²×C₃	semidirect
250. C₂×#121	C₂²×C₃	semidirect
255. C₂²×C₄⋊C₄	C₂²×C₃	semidirect
260. #400	C₂²×C₃	semidirect
261. #400	C₂²×C₃	semidirect
262. #398	C₂²×C₃	semidirect
269. #397	C₂²×C₃	semidirect
270. #397	C₂²×C₃	semidirect
271. #397	C₂²×C₃	semidirect
272. #397	C₂²×C₃	semidirect
273. #397	C₂²×C₃	semidirect
274. #397	C₂²×C₃	semidirect
275. #397	C₂²×C₃	semidirect
276. #397	C₂²×C₃	semidirect
277. #395	C₂²×C₃	semidirect
278. #395	C₂²×C₃	semidirect
279. #395	C₂²×C₃	semidirect
283. #394	C₂²×C₃	semidirect
284. #394	C₂²×C₃	semidirect
285. #394	C₂²×C₃	semidirect
286. #394	C₂²×C₃	semidirect
287. #394	C₂²×C₃	semidirect
288. #393	C₂²×C₃	semidirect
290. #392	C₂²×C₃	semidirect
291. #392	C₂²×C₃	semidirect
292. #388	C₂²×C₃	semidirect
293. #387	C₂²×C₃	semidirect
294. #387	C₂²×C₃	semidirect
295. #387	C₂²×C₃	semidirect
300. #386	C₂²×C₃	semidirect
301. #386	C₂²×C₃	semidirect
302. #386	C₂²×C₃	semidirect
303. #386	C₂²×C₃	semidirect
304. #386	C₂²×C₃	semidirect
305. #386	C₂²×C₃	semidirect
306. #386	C₂²×C₃	semidirect
307. #385	C₂²×C₃	semidirect
308. #385	C₂²×C₃	semidirect
309. #385	C₂²×C₃	semidirect
310. #385	C₂²×C₃	semidirect
311. #385	C₂²×C₃	semidirect
312. #385	C₂²×C₃	semidirect
313. #385	C₂²×C₃	semidirect
314. #385	C₂²×C₃	semidirect
317. #381	C₂²×C₃	semidirect
318. #381	C₂²×C₃	semidirect
319. #381	C₂²×C₃	semidirect
320. #380	C₂²×C₃	semidirect
321. #380	C₂²×C₃	semidirect
322. #380	C₂²×C₃	semidirect
325. C₂×#95	C₂²×C₃	semidirect
326. C₂×#95	C₂²×C₃	semidirect
461. C₂²×D₄	C₃×D₄	semidirect
992. C₃	#41404	direct (N × H)

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroup	index
C₂×C₃×#546	2
C₃×#2817	2
C₃×#2812	2
C₃×#2717	2
C₃×#2708	2
C₃×#2688	2
C₃×#2686	2
C₃×#2638	2
C₃×#2622	2
C₃×#2617	2
C₃×#2600	2
C₃×#2483	2
C₃×#2444	2
C₃×#2430	2
C₃×#2419	2
C₃×#2412	2
C₃×#2406	2
C₂×C₃×#397	2
C₃×#2308	2
#41404	3

Subgroups — C3×#41404 #10660011

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃×#41404 #10660011